[seqfan] Re: My page on the Wiki for detected relations between sequences

Thomas Baruchel baruchel at gmx.com
Tue Dec 19 10:43:37 CET 2017

On Tue, 18 Dec 2017, israel at math.ubc.ca wrote:
> I suggest you explain your notation on that page.  For example, does
> A133010 A133011 A135297 A286707    -->    1 1 -1 1    (4)
> mean A133010(n) + A133011(n) - A135297(n) + A286707(n) = 0?
> What is the 4?

I added some explanations; the 4 is the norm 1^2 + 1^2 + (-1)^2 + 1^2. The other
numbers are coefficients as you understood it.

> This may be a rather unfortunate example to start with (or perhaps we 
> should say, it nicely illustrates the pitfalls of these algorithms). It is

Yes, I removed this example; this is the purpose of this list; I put some raw results
on it for later examinations either by me or by anybody interested. I shouldn't anyway
have put this one on the page for at least another reason: I was aware that results
with coefficients being all 1 or -1 are generally not interesting (they often are
trivial; of course it can be that similar sequences are involoved in such results).

Results with more "exotic" coefficients should be more interesting; of course they
need to be studied: they can be trivial or not; most of them should be "true" however,
my tool checks the results for 32 initial terms (in order to spare computing time),
which is obviously not a mathematical "proof", but having spent much time with such
"detection" algorithm, I can tell that detecting something very interesting is much
more challenging that being sure no false result occur from time to time.

This morning I added some more results with the name "euler" in them.

I tuned my own compiled versions of the tool to display detected relations only if
the relation involves at least 4 different sequences (maybe it is a wrong idea and
some relations with 3 sequences could be interesting). I generally can get about 50
more or less significant results on my Raspberry Pi device within a few hours. If two or
three interesting relations occur after some days of computation, I could say it was
still worth it.

Thank you for your advices;

best regards,

Thomas Baruchel

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